Morawiecki told reporters that the government's inoculation programme would help Poland achieve herd immunity, and avoid further lockdowns and economic problems.
"Today is a time of renaissance for the economy. Let us not allow October and November 2021 to bring bad news again. We have the means to prevent this - the vaccination programme," he added.
The government on Saturday unveiled an ambitious "Polish New Deal" programme to help the economy recover from the pandemic, while also promising more support for young families and a cash injection for public healthcare.
Morawiecki at the end of last month announced that a swathe of COVID restrictions on daily life would be eased in several stages after a fall in new infections and amid increased supplies of vaccines.
Shopping malls, DIY stores, museums and art galleries around the country were allowed to reopen in early May, with limits on the number of clients they can admit at one time.
Poland on Monday reported 1,109 new coronavirus infections, down from a high of 35,251 on April 1.
Over 11.5 million first doses of COVID-19 vaccines have been administered so far, while almost 4.8 million people have been fully inoculated, according to the health ministry.